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Changing modules to more taxing ones / sitting in lectures?

[INDENT]I've recently decided that I definitely want to carry on studying mathematics and do a PhD after my Masters degree. As a result I might make a couple of changes to my modules as I've decided on for my third year.

My current module choices are (for the upcoming year):

Quantum Mechanics I (Physics elective)
Scientific Programming in C (Physics elective)
Fluid Dynamics
Research in Mathematical Sciences
Partial Differential Equations
Nonlinear Systems and Control
Complex Analysis
Mathematics of Climate Change.

The general direction of my studies is towards applications of differential equations and vector calculus, so there is comparatively less pure mathematics than I've previously encountered. These module choices were sparked by a possible interest in working in climate, but mainly to study things such as chaos theory further on in academia.

However, I'm debating changing a couple of modules. I've thought about changing Scientific Programming in C to Electromagnetism I (Physics elective), and also to change Mathematics of Climate Change to Modern Algebra or Stochastic Processes. Both the climate and programming modules are very light on mathematics from what I hear.

Basically the proposed changes to my modules would be to make them more theoretical/pure, partly because I feel like I want to be stretched a bit more and overcome my weakness with mathematical proof (as I still struggle with things like proof in analysis and algebra) which I feel hasn't been sorted out yet. That is my motivation for wanting to do more stretching modules, sort of to get as much out my university experience as possible. Also, I sort of think that an algebra course will further cement the pure mathematics I've already covered and also round it off (as Galois theory is covered in the module, thus providing a link between fields and groups which I have done in separate modules). However, on paper, my original choices of the modules looks more useful to employers and for needing to stay in academia. On the grounds of usefulness, I may actually take exams in the more useful ones but sit in the lectures of the other modules because they seem interesting. There are more modules that I wanted to do than options I had available.

There are some questions I have:

- Is it better to choose modules that are more stretching?
- Is it a good idea to take modules that are a bit less useful even if they are more theoretical/interesting?
- Is it a good idea to sit in modules you're not actually taking?[/INDENT]

Reply 1

.ACS.

Original post by OL1V3R

...

You need to decide whether you are doing a PhD after your MMath or may go into the world of work, and if so, which career route.

If you are going into academia, or a career requiring specific modules, then it is best to choose modules that are best suited to preparing you for that route. If to do the PhD you need more pure maths, then go for that. If you don't, then choose the ones which will best prepare you for your PhD.

It is always worth speaking to lecturers to get an idea of what they think. They are the best people to ask since they will have been in your shoes only a few decades before. But also they are the ones who supervise PhD students and so realise how important/unimportant relevant modules are to academic research.

As for sitting in on modules but not taking the exam, go for it. I have done that with plenty of modules, ranging from those I am interested in such but will have no real use to me such as political theory to those which I will use in my career in the future such as stochastic modelling.